Science Daily  6, 2022 Researchers in Japan provide simple theorems that show what kinds of long-range entanglement can survive at nonzero temperatures. At temperatures above absolute zero, quantum entanglement must contend with thermal jostling of particles, which is detrimental to long-range entanglement persisting at sufficiently high temperatures. Unlike high-temperature phases, however, there are relatively low temperatures in which not all long-range quantum effects are strictly prohibited, and long-range entanglement can survive even at room temperatures. They proved that entanglement between two subsystems has a finite characteristic length scale at arbitrary temperatures regardless of the system details and the spatial dimension. […]